Category: Technical diagnostics and controllable systems

Authors:

Abdullaev R. B.

Annotation:
Probabilistic features of some polynomial codes in case of fault occurrence in data bits with faultlessness of check bits, the latter being topical for the systems of technical diagnosis of automation devices, are considered in the article. The method of calculating probability of undetectable errors by the given codes was described depending on the probability of error detection failure in one data bit. It was demonstrated that together with the data bit length increase, probability of occurrence of low-multiplicity errors is reduced. The polynomials by means of which codes with the best indices of probabilistic features are built were singled out of all polynomials producing codes with the same number of check bits. The dependency of probability of undetectable maximum-multiplicity errors under various failure-free operation indices of circuits under diagnosis was established. Probabilistic features were calculated according to the types of undetectable errors of polynomial codes under study. Generator polynomials were singled out by means of which codes with the minimum probabilistic indices for detection failure of certain types of errors are built. Polynomial codes can be divided into classes of codes with constant number of check bits. Therefore, the former should be compared with modular summation codes, which also possess constant number of check bits, according to their characteristics. To achieve this, probabilistic features of summation codes were calculated and compared with characteristics of polynomial codes. Calculations have shown that in case of different probability values of one data bit distortion, occurrence probability for undetectable errors in polynomial codes is much lower than in summation codes. During the research a full catalogue of probabilistic features of codes with k=2 and k=3 polynomial codes and summation codes has been compiled. The catalogue may be used for the analysis of probabilistic characteristics of other separable codes applied for the purposes of technical diagnosis.

Key words:
Concurrent checking, undetectable error, polynomial code, error detection probability in the data vector of a code, probabilistic feature of the polynomial code


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